Further Results on Differential Stability of Convex Optimization Problems

被引：14

作者：

Duong Thi Viet An ^{[1
,2
]}

Yao, Jen-Chih ^{[3
,4
]}

机构：

[1] Thai Nguyen Univ, Dept Math & Informat, Coll Sci, Thai Nguyen City, Vietnam

[2] Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung 804, Taiwan

[3] China Med Univ, Ctr Gen Educ, Taichung 40402, Taiwan

[4] China Med Univ Hosp, Res Ctr Interneural Comp, Taichung 40447, Taiwan

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2016年 / 170卷 / 01期

关键词：

Parametric convex programming; Optimal value function; Subdifferential; Singular subdifferential; Aubin's regularity condition; INCLUSION CONSTRAINTS; MARGINAL FUNCTION;

D O I：

10.1007/s10957-016-0900-7

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

As a complement to a recent paper by An and Yen (Appl Anal 94:108-128, 2015) on subdifferentials of the optimal value function in parametric convex programming under inclusion constraints and functional constraints, this paper studies the differential stability of convex optimization problems under a regularity condition of Aubin's type (Aubin in Optima and equilibria: an introduction to nonlinear analysis. Springer, New York, 1998). By a suitable sum rule for convex subdifferentials, we obtain exact formulas for the subdifferential and singular subdifferential of the optimal value function. Illustrative examples and a detailed comparison of our results with those of the above-mentioned paper are given.

引用

页码：28 / 42

页数：15

共 17 条

[1] Differential stability of convex optimization problems under inclusion constraints [J].